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21 May 1993 Precision of morphological estimation
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Mean-absolute-error-optimal, finite-observation, translation-invariant, binary-image filters have previously been characterized in terms of morphological representations: increasing filters as unions of erosions and nonincreasing filters as unions of hit-or-miss operators. Based upon these characterizations, (sub)optimal filters have been designed via image-process realizations. The present paper considers the precision of filter estimation via realizations. A key point: while precision deteriorates for both erosion and hit-or-miss filters as window size increases, the number of image realizations required to obtain good estimation in erosion-filter design can be much less than the number required for hit-or-miss-filter design. Thus, while in theory optimal hit-or-miss filtering is better because the unconstrained optimal hit-or-miss filter is the conditional expectation, owing to estimation error it is very possible that estimated optimal erosion filters are better than estimated optimal hit-or-miss filters.
© (1993) COPYRIGHT Society of Photo-Optical Instrumentation Engineers (SPIE). Downloading of the abstract is permitted for personal use only.
Edward R. Dougherty and Robert P. Loce "Precision of morphological estimation", Proc. SPIE 1902, Nonlinear Image Processing IV, (21 May 1993);

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